Question: What number could replace $a$ below? $\dfrac{1}{2} = \dfrac{3}{a}$
Solution: The fraction on the left represents 1 out of 2 slices of a rectangular cake. How many total slices would we need if we want the same amount of cake in 3 slices? We would need to cut the cake into 6 slices. $\dfrac{1}{2} = \dfrac{3}{6}$ and so the answer is $6$ Another way to get the answer is to multiply by $\dfrac{3}{3}$ $\dfrac{3}{3} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{2} \times \dfrac{3}{3} = \dfrac{3}{6} $ so our answer is $6$.